# Exponential equation + geometric progression - examples

- Crystal

Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g? - Compound interest

Calculate time when deposit in the bank with interest 2.5% p.a. doubles. - Demographics

The population grew in the city in 10 years from 42000 to 54500. What is the average annual percentage increase of population? - Geometric sequence 3

In geometric sequence is a_{8}= 312500; a_{11}= 39062500; s_{n}=1953124. Calculate the first item a_{1}, quotient q and n - number of members by their sum s_n. - Sequence

Calculate what member of the sequence specified by ? has value 86. - Half life

Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes. - To the cinema

Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in. - Geometric sequence

In the geometric sequence is a_{4}= 20 a_{9}= -160. Calculate the first member a_{1}and quotient q. - Insert into GP

Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert? - Geometric progression

In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217. - Microorganisms

The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation. - Radioactive material

A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years? - Investment

1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?

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